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Journal of Mathematical Physics / Volume 21 / Issue 1

J. Math. Phys. 21, 6 (1980); http://dx.doi.org/10.1063/1.524310 (8 pages)

Asymptotic approximations for modified Bessel functions

P. Kasperkovitz

Institut für Theoretische Physik, TU Wien, A–1040 Karlsplatz 13, Austria

The behavior of a qν(x) =Iν(x)/Iνa(x), where Iν is a modified Bessel function with integral or half‐integral index ν and Iνa the leading term of its asymptotic series, is investigated for x≫1. It is shown that qν(x) may be approximated by eν(x) =exp(−ν2/2x), the difference rν(x) =qν(x)−eν(x) being of order x−1/4. Bounds for rν(x) depending only on x are derived for each of the two classes of ν’s and an application of these results in scattering theory is indicated.

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.524310

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

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